US8109816B1 - Method and apparatus for measurement and analysis of a golf swing - Google Patents

Abstract

A method for analyzing at least one golf swing parameter using a plurality of accelerometers located proximate the distal ends of a golf club, a signal processing and display system utilizing a double pendulum model of a golf club swing, said model for describing swing parameters and having an upper portion, a pivot point and a lower portion, the method comprising the steps of entering initial swing conditions and golf club parameters; performing a swing and collecting data from the accelerometers; determining a differential mode signal from the acceleration data; calculating the pivot point location relative to each accelerometer using the accelerometer data; calculating a common mode signal using the pivot point; and determining at least one golf swing parameter as a function of time using the common mode signal. In a specific embodiment, the step of calculating the pivot point location relative to each accelerometer comprises the step of minimizing the contribution of the common mode signal into an accelerometer signal comprising the differential mode signal and the common mode signal. The method may also comprise the step of displaying the at least one golf swing parameter.

Description

BACKGROUND OF THE INVENTION

This invention relates to a system and method for measuring and analyzing acceleration data from a golf club and for applying said data to golf swing analysis.

The use of electronics in the shaft or club head of a golf club to measure golf swing characteristics has been the subject of considerable past work. Modern implementations offer a large number of sensors and computational power all concealed within the shaft. Over time, the tendency has been to make ever more sophisticated measurements in an effort to obtain increasingly detailed understanding of the golf swing.

U.S. Pat. Nos. 6,648,769, 6,638,175, 6,402,634 and 6,224,493 describe instrumented golf clubs that use accelerometers and strain gages mounted in the club head and an angular rate sensor to measure the angular speed of the grip area of the club.

U.S. Pat. Nos. 6,658,371, 6,611,792, 6,490,542, 6,385,559 and 6,192,323 describe methods for matching golfers with a driver and ball by measuring a golfer's club head speed and comparing that measured data with recorded sets of data that correlate a few key variables that can aid in matching golfers with the most suitable club and ball.

However, as will be seen below, further advances in the state of the art are desirable and believed to be achieved by the present invention.

OBJECTIVES AND SUMMARY OF THE INVENTION

It is thus an objective of the present invention to improve the state of the art.

It is another objective to provide improved measurement and analyses methodologies for a golf swing.

Another objective of the present invention is the calculation, identification and display of key parameters of the golf swing using a double pendulum model of the golf swing so that they can be used to improve a golfer's performance.

Other objectives and advantages of the present invention will be described below and/or be obvious in view of the disclosure below.

The present invention accordingly comprises the features of construction, combination of elements, arrangement of parts and sequence of steps which will be exemplified in the construction, illustration and description hereinafter set forth, and the scope of the invention will be indicated by the claims.

To that end, in a preferred embodiment, the present invention generally speaking, is directed to a method for analyzing at least one golf swing parameter using a plurality of accelerometers located at distal ends of a golf club, a signal processing and display system utilizing a double pendulum model of a golf club swing, said model for describing swing parameters and having an upper portion, a pivot and a lower portion, the method comprising the steps of entering initial swing conditions and golf club parameters; performing a swing and collecting data from the accelerometers; determining a differential mode signal from the acceleration data; calculating the pivot point location relative to each accelerometer using the accelerometer data; calculating a common mode signal using the pivot point and acceleration data; and determining at least one golf swing parameter as a function of time using the common mode signal.

In another embodiment, the present invention is directed to a method for analyzing at least one golf swing parameter using (i) an instrumented golf club having two accelerometers located at respective distal ends of a golf club, (ii) data collection means and (iii) computer analysis means running a program based on a double pendulum model of a golf club swing, the method comprising the steps of entering initial swing conditions and golf club parameters; performing a swing and collecting data from the accelerometers; determining a differential mode signal from the acceleration data; calculating the pivot point location relative to each accelerometer using the accelerometer data; calculating a common mode signal using the pivot point and acceleration data; and determining at least one golf swing parameter as a function of time using the common mode signal.

In yet another preferred embodiment, a method for analyzing at least one motion parameter of an elongated member moving relative to a pivot point using a plurality of accelerometers located at proximate distal ends of the elongated member, a signal processing and display system utilizing a model relating the motion of the pivot point and accelerometers to a reference point is provided, the method comprising the steps of entering initial positional and physical parameters of the elongated member; moving the elongated member about the pivot point and collecting data from the accelerometers; determining a differential mode signal from the acceleration data; calculating the pivot point location relative to each accelerometer using the accelerometer data; calculating a common mode signal using the pivot point location relative to each accelerometer; and determining at least one parameter of motion for the elongated member as a function of time using the common mode signal.

And, in yet another preferred embodiment, a method is provided for analyzing at least one motion parameter of a swinging elongated member using a plurality of accelerometers located at proximate distal ends of the elongated member, a signal processing and display system utilizing a double pendulum model of the swinging elongated member, said model having an upper portion, a pivot point and a lower portion, the method comprising the steps of entering initial positional and physical conditions of the elongated member; swinging the elongated member and collecting data from the accelerometers; determining a differential mode signal from the acceleration data; calculating the pivot point location relative to each accelerometer using the accelerometer data; calculating a common mode signal using the pivot point location relative to each accelerometer; and determining at least one motion parameter of the elongated member as a function of time using the common mode signal.

In a specific embodiment, the measurement system preferably comprises two accelerometers mounted in the shaft of a golf club with the direction of maximum sensitivity oriented along the axis of the shaft. One accelerometer is located under the grip, preferably near where the hands would be located. The other is located further down the shaft nearer to the club head.

The two accelerometers yield a common mode signal and a differential mode signal. The common mode signal contains components that are present in both accelerometers while the differential mode signal is the difference between the accelerometer values and is proportional to the rotational kinetic energy of the golf club. An important objective of the present invention is the automatic location of a pivot point of the double pendulum to substantially eliminate mixing of common mode accelerometer signals with differential mode accelerometer signals and therefore provide improved analysis of golf swing parameters that include common mode signal components.

BRIEF DESCRIPTION OF THE DRAWINGS

For a fuller understanding of the invention, reference is made to the following description taken in connection with the accompanying figures, in which:

FIG. 1 is an illustration of a golf swing analysis system constructed in accordance with the present invention;

FIG. 2 is a block diagram of the electronics located in a golf club of a preferred embodiment of the present invention;

FIG. 3 is a block diagram of a wireless interface and circuits of a signal processor and display system;

FIGS. 4aand4bshow raw data for the two accelerometers S₁and S₂;

FIG. 5 gives the geometry of the motion of a rigid rod in a fixed plane;

FIG. 6 shows the geometry of a double pendulum model representing a golfer and club;

FIGS. 7aand7bshow a differential mode signal g(t) and common mode signal f(t) calculated from the data displayed inFIGS. 4aand4b;

FIG. 8 shows a preferred flow chart for the present invention;

FIG. 9 shows the angular position of the upper and lower portions of the double pendulum as a function of time;

FIG. 10 shows the backswing and down swing positions of the upper and lower portions of a double pendulum representing the player and club during a golf swing; and

FIG. 11 shows a display of the present invention.

While all features may not be labeled in each Figure, all elements with like reference numerals refer to similar or identical parts.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The entire contents of U.S. Patent Application 2006/0063600, also by Robert Grober, is hereby incorporated into this application by reference as if set forth in its entirety.

Reference is first made toFIGS. 1 and 2 wherein a measurement and display system constructed in accordance with the present invention is generally shown at100. A golf club constructed in accordance with the present invention is indicated generally at200 and awireless interface310 and associated signal processing anddisplay system390 are generally shown at300.Wireless interface310 provides a wireless link betweenclub200 and signal processing anddisplay system390.

The golf club at200 comprises an elongated member, generally indicated at215, which itself comprises at least ashaft215 and aclub head230.Golf club200 also comprises afirst accelerometer220 generally located nearclub grip222 and asecond accelerometer225 located closer toclub head230. Both accelerometers are preferably coupled tomember215. In thepreferred embodiment accelerometer220 is an Analog Devices ADXL78 andaccelerometer225 is an Analog Devices ADXL193. The foregoing positions more than satisfy the understanding that the accelerometers are located proximate the distal ends of the shaft.

Accelerometers220 and225 monitor accelerations along the axis ofmember215 as a golfer (not shown)swings club200. Preferably located inmember215 is additional circuitry, generally indicated at245, comprising two (2) A/D converters254 and255 respectively operatively coupled toaccelerometers220 and225, amicroprocessor260 coupled toconverters254,255 and awireless transceiver265 coupled between the output ofmicrocontroller260 andantenna235.

As shown inFIG. 2, the analog outputs of the accelerometers are fed to A/D converters254 and255 where they are converted into digital data streams and fed viaserial link262 tomicroprocessor260 for processing. The preferred embodiment includes Microchip MCP3201 12 bit A/D converters to convert the analog output ofaccelerometers220 and225 into digital data streams that are fed tomicroprocessor260, which preferably is a Microchip 8 bit microcontroller, the PIC 16F873A.

Microprocessor260 supervises the collection of data from the A/D converters254 and255 and formats the resulting 12 bit NRZ data for transmission to signal processing anddisplay system390 viatransceiver265,antenna235 and wireless interface310 (shown inFIG. 3). In alternate embodiments collected data can be stored on a memory card or thumb drive and removed/disconnected fromclub200 and inserted into signal processing anddisplay system390 for processing.

Transceiver265 is preferably a Chipcon CC1000 configured to receive the NRZ serial data frommicroprocessor260, reformat the data into synchronous Manchester coding and preferably feedantenna235 at 915 MHZ. Transceiver initialization values, which include data formatting, frequency selection, etc. are stored in flash memory inmicroprocessor260 and fed totransceiver265 byserial link266. The initialization data may also originate in signal processing anddisplay system390 and fed to transceiver235 viainterface310. The acceleration data stream frommicrocontroller260 is sent totransceiver265 byserial link264.

As shown inFIG. 3,wireless interface310 receives the transmitted data viaantenna315 and, in a wired manner known to those skilled in the art, provides the data to signal processing anddisplay system390. Signal processing anddisplay system390 preferably comprises a Windows XP based laptop wherein a software program based on the flowchart ofFIG. 8 and described herein is executed. This program is preferably programmed in the C/C++ programming language or assembly language where execution speed is important. Signal processing anddisplay system390 is suitably equipped withkeyboard322, display360 having adisplay area362, and one or more USB ports326 (with connector and interface circuits) for receiving and sending data to/fromwireless interface310 and receiving external or thumb drives (not shown). In an alternate embodiment signal processing anddisplay system390 andgolf club200 are equipped with a compatible wireless interface so thatwireless interface310 andtransceiver235 are not needed as a separate unit.

FIG. 3 is a blockdiagram showing transceiver330 andmicrocontroller335 ofwireless interface310 and signal processing anddisplay system390 which is generally shown at300. The 12 bit data transmitted bytransceiver265 andantenna235 is received byantenna315 and demodulated back to NRZ code bytransceiver330 and fed tomicrocontroller335 via a NRZ serial stream.Serial busses332 and334 provide communications betweentransceiver330 andmicrocontroller335 which is preferably a PIC 18F4550.Microcontroller335 with associatedUSP port326 communicates with signal processing anddisplay system390 viaUSB cable337 and anotherUSB port326 in communication withbus340.Internal data buss340 communicates withring buffer342, which is itself part ofRAM341,ROM344, aCPU346, CD drive348,Hard Drive350 anddisplay360. In analternate embodiment microcontroller335 communicates with signal processing anddisplay system390 using a conventional serial port.

Accelerometer Measurements

Shown inFIG. 4 is raw data from accelerometer225 (labeled S₁) and from accelerometer220 (labeled S₂) during a single golf swing. The data is transmitted fromclub200 and received bywireless interface310 and fed to signal processing anddisplay system390 as described above. S₁is from 120g accelerometer225 located near theclub head230 end ofshaft215. S₂is from 50g accelerometer220 located undergrip222 ofclub200. The data used to generateFIGS. 4(a) and4(b) are identical, with (b) being scaled so that the details at small accelerations are more visible.

In a preferred embodiment of the invention the zero of the time axis inFIG. 4 can be somewhat arbitrary and roughly corresponds to the point where theclub head230 passes a tee (not shown) holding a golf ball230 (also not shown). The data inFIG. 4 was taken while swinging a club but not hitting a ball. This was done to prevent the data from being corrupted by the shock of impact. In alternative embodiments an inductive sensor or optical sensor or the like can be used to establish a substantially exact position at which impact would occur without concern for transients disturbing accelerometer data. Alternatively, and as discussed below, a lightweight plastic ball may be used to provide more realism and in this case an acoustic sensor is used to sense impact without affecting accelerometer data.

The data ofFIG. 4 consist of 600 pairs of points, each pair taken at 4.42 msec intervals. The data has been normalized such that the y-axis is calibrated in units of gravitational acceleration, 9.8 m/s².

Data similar to that used to generate inFIG. 4 are reduced and processed in accordance with the flow chart ofFIG. 8 which shows the program flow used to implement the analysis disclosed in the paragraphs that follow.

Rotational Analysis of a Golf Club

The generalized two-dimensional geometry and motion associated with a point on a golf club in a plane is shown inFIG. 5. All points and motions are referenced to a fixed, inertial, Cartesian coordinate system in the plane of the golf swing with the {circumflex over (x)}-axis aligned along the direction of gravitational acceleration. Likewise all calculations and notations related to time dependent parameters are shown using continuous time notation. One skilled in the art would recognize however that the invention uses sampled data so that calculations would preferably be accomplished in the digital domain.

The position of the club in space is defined by the coordinates {right arrow over (R)}₀=(Y₀,X₀) of the reference point {right arrow over (R)}₀on the club and the angle φ of the club with respect to the {circumflex over (x)}-axis. The preferred choice for the point {right arrow over (R)}₀is that point about which the club rotates. The distance to the general point {right arrow over (r)}₁on the shaft is measured relative to the reference point {right arrow over (R)}₀. The coordinates of {right arrow over (r)}₁are given as
{right arrow over (r)}₁=(X₀+{right arrow over (r)}₁cos φ){circumflex over (x)}+(Y₀+r₁sin φ)ŷ  (1)
One determines the generalized acceleration of the point {right arrow over (r)}₁as
{umlaut over ({right arrow over (r)}₁=({umlaut over (X)}₀−r₁{dot over (φ)}²cos φ−r₁{umlaut over (φ)} sin φ){circumflex over (x)}+(Ÿ₀−r₁{dot over (φ)}²sin φ+r₁{umlaut over (φ)} cos φ)ŷ  (2)
It is useful to rewrite this equation in terms of the in terms of the {circumflex over (r)}−{circumflex over (φ)} coordinate system, as indicated inFIG. 5. Using the relations
{circumflex over (x)}={circumflex over (r)}cos φ−{circumflex over (φ)} sin φ  (3a)
ŷ={circumflex over (r)}sin φ+{circumflex over (φ)} cos φ  (3b)
one obtains
{umlaut over ({right arrow over (r)}₁=({umlaut over (X)}₀cos φ+Ÿ₀sin φ−r₁{dot over (φ)}²){circumflex over (r)}+(−{umlaut over (X)}₀sin φ+Ÿ₀cos φ+r₁{umlaut over (φ)}){circumflex over (φ)}  (4)

Accelerometers225 and220 are located alongshaft215 at positions {right arrow over (r)}₁and {right arrow over (r)}₂which are measured relative to {right arrow over (R)}₀onshaft215.Accelerometers225 and220 are oriented to be most sensitive to accelerations along the axis ofshaft215 and to yield a positive centripetal acceleration as thegolf club200 is swung. The accelerations measured byaccelerometers225 and220 along the {right arrow over (r)}-axis are S₁and S₂respectively and have values of:
S₁=−{circumflex over (r)}·{umlaut over ({right arrow over (r)}₁=−{umlaut over (X)}₀cos φ−Ÿ₀sin φ+r₁{dot over (φ)}²  (5a)
S₂=−{circumflex over (r)}·{umlaut over ({right arrow over (r)}₂=−{umlaut over (X)}₀cos φ−Ÿ₀sin φ+r₂{dot over (φ)}²  (5b)
Because these measurements are made in the presence of earth's gravitational field, the equations above are preferably adjusted to include this effect, yielding the expressions:
S₁=−{right arrow over (r)}·{umlaut over ({right arrow over (r)}₁=−{umlaut over (X)}₀cos φ−Ÿ₀sin φ+r₁{dot over (φ)}²+G*cos φ  (6a)
S₂=−{right arrow over (r)}·{umlaut over ({right arrow over (r)}₂=−{umlaut over (X)}₀cos φ−Ÿ₀sin φ+r₂{dot over (φ)}²+G*cos φ  (6b)
where G* is the effective gravitational acceleration in the plane of the golf swing.

These two signals are preferably written in terms of two signals. The first is a common mode signal (contribution to accelerometer output value that is common to the output of both accelerometers), and that is f(t)=−{umlaut over (X)}₀cos φ−Ÿ₀sin φ+G* cos φ, and the second is a differential mode (the difference between the outputs of both accelerometers) resulting value g(t)=(r₁−r₂){dot over (φ)}². Rewriting S₁and S₂in a generic form gives:

$\begin{array}{cc}{\mathrm{<figure-callout\; label="S"\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">S</figure-callout>}}_1=f\left(t\right)+\frac{r_1}{r_1-{\mathrm{<figure-callout\; label="r"\; filenames="US08109816-20120207-D00005.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}g\left(t\right);\mathrm{and}& \left(7a\right)\\ {\mathrm{<figure-callout\; label="S"\; filenames="US08109816-20120207-D00005.png"\; state="\{\{state\}\}">S</figure-callout>}}_2=f\left(t\right)+\frac{r_2}{r_1-{\mathrm{<figure-callout\; label="r"\; filenames="US08109816-20120207-D00005.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}g\left(t\right)& \left(7b\right)\end{array}$

The differential mode signal, g(t), is recovered by taking the difference of the two signals (after appropriate scaling), S₁−S₂=g(t)=(r₁−r₂){dot over (φ)}². Because the separation betweenaccelerometers225 and220, r₁−r₂, is easily measured, knowledge of g(t) permits the calculation of φ(t) as discussed below.

While the differential mode signal is substantially independent of the choice of the point {right arrow over (R)}₀, the common mode signal depends strongly on the choice of the point {right arrow over (R)}₀. Thus, the choice of the point {right arrow over (R)}₀determines how much of the differential mode signal is mixed into the calculated common mode signal and therefore effects the calculation of φ(t). This sensitivity to {right arrow over (R)}₀makes recovering f(t) more difficult and requires consideration of the motion of point {right arrow over (R)}₀=(Y₀,X₀). To this end it has been discovered that the use of a double pendulum model gives good results.

Use of the double pendulum in an analysis of the golf swing was developed by T. P. Jorgensen. The model he used is shown inFIG. 6 and reasonably represents the golf swing of capable golfers. The angle θ defines the angle of an upper portion of length l₀(the lower termination of the upper portion with length l₀is at the point {right arrow over (R)}₀) with respect to the x-axis and φ defines the angle of the lower portion (the club200) of length l_c, with respect to the x-axis. The upper portion represents the link between the club and the golfer's body (not shown).

The angle β defines the angle of the lower portion with respect to the upper portion, and is interpreted as the wrist cocking angle. The model assumes no translational motion of the center of the swing which is at the upper point of the upper portion l₀. Additionally, the model assumes a rigid shaft forclub200 as it is known that shaft dynamics yield second order effects.

The relevantportion golf club200 is modeled as a rigid rod having a length l_c, that is measured from the point R₀to approximately the center ofclub head230. The orientation ofgolf club200 is preferably measured by the angle β=θ−φ, which, as previously noted, roughly corresponds to the angle through which the wrists are cocked.

Theaccelerometers225 and220 are oriented along the axis of thegolf club200 with their positions along the club also measured from the hinged point R₀between the upper and lower portions of the pendulum and given by lengths r₁and r₂(seeFIG. 5). Following the analysis above, their position in space are given as:
{right arrow over (r)}₁=(l₀cos θ+r₁cos φ){circumflex over (x)}+(l₀sin θ+r₁sin φ)ŷ  (8a)
{right arrow over (r)}₂=(l₀cos θ+r₂cos φ){circumflex over (x)}+(l₀sin θ+r₂sin φ)ŷ  (8b)

One can determine the generalized acceleration of the two points {right arrow over (r)}₁and {right arrow over (r)}₂as:

$\begin{array}{cc}{\ddot{\overrightarrow{r}}}_1=-\left({\mathrm{<figure-callout\; label="l"\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">l</figure-callout>}}_0{\stackrel{.}{\theta }}^2\cos \theta +{\mathrm{<figure-callout\; label="l"\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">l</figure-callout>}}_0\ddot{\theta }\sin \theta +{\mathrm{<figure-callout\; label="r"\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">r</figure-callout>}}_1{\stackrel{.}{\varphi }}^2\cos \varphi +{\mathrm{<figure-callout\; label="r"\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">r</figure-callout>}}_1\ddot{\varphi }\sin \varphi \right)\hat{x}-\left({\mathrm{<figure-callout\; label="l"\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">l</figure-callout>}}_0{\stackrel{.}{\theta }}^2\sin \theta -{\mathrm{<figure-callout\; label="l"\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">l</figure-callout>}}_0\ddot{\theta }\cos \theta +{\mathrm{<figure-callout\; label="r"\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">r</figure-callout>}}_1{\stackrel{.}{\varphi }}^2\sin \varphi -{\mathrm{<figure-callout\; label="r"\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">r</figure-callout>}}_1\ddot{\varphi }\cos \varphi \right)\hat{y}& \left(9a\right)\\ {\ddot{\overrightarrow{r}}}_2=-\left({\mathrm{<figure-callout\; label="l"\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">l</figure-callout>}}_0{\stackrel{.}{\theta }}^2\cos \theta +{\mathrm{<figure-callout\; label="l"\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">l</figure-callout>}}_0\ddot{\theta }\sin \theta +{\mathrm{<figure-callout\; label="r"\; filenames="US08109816-20120207-D00005.png"\; state="\{\{state\}\}">r</figure-callout>}}_2{\stackrel{.}{\varphi }}^2\cos \varphi +{\mathrm{<figure-callout\; label="r"\; filenames="US08109816-20120207-D00005.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\ddot{\varphi }\sin \varphi \right)\hat{x}-\left({\mathrm{<figure-callout\; label="l"\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">l</figure-callout>}}_0{\stackrel{.}{\theta }}^2\sin \theta -{\mathrm{<figure-callout\; label="l"\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">l</figure-callout>}}_0\ddot{\theta }\cos \theta +{\mathrm{<figure-callout\; label="r"\; filenames="US08109816-20120207-D00005.png"\; state="\{\{state\}\}">r</figure-callout>}}_2{\stackrel{.}{\varphi }}^2\sin \varphi -{\mathrm{<figure-callout\; label="r"\; filenames="US08109816-20120207-D00005.png"\; state="\{\{state\}\}">r</figure-callout>}}_2\ddot{\varphi }\cos \varphi \right)\hat{y}& \left(9b\right)\end{array}$

It is useful to rewrite the above the equations in terms of the r−φ coordinate system attached to the golf club with the r-axis aligned along the shaft. Using the relations:
{circumflex over (x)}={circumflex over (r)}cos φ−{circumflex over (φ)} sin φ  (10a)
ŷ={circumflex over (r)}sin φ+{circumflex over (φ)} cos φ  (10b)
and the trigonometric identities
sin θ cos φ−cos θ sin φ=sin(θ−φ)  (11a)
sin θ sin φ+cos θ cos φ=cos(θ−φ)  (11b)
one obtains
{umlaut over ({right arrow over (r)}₁=−(r₁{dot over (φ)}²+l₀{dot over (θ)}²cos β+l₀{umlaut over (θ)} sin β){circumflex over (r)}+(r₁{umlaut over (φ)}−l₀{dot over (θ)}²sin β+l₀{umlaut over (θ)} cos β){circumflex over (φ)}  (12a)
{umlaut over ({right arrow over (r)}₂=−(r₁{dot over (φ)}²+l₀{dot over (θ)}²cos β+l₀{umlaut over (θ)} sin β){circumflex over (r)}+(r₂{umlaut over (φ)}−l₀{dot over (θ)}²sin β+l₀{umlaut over (θ)} cos β){circumflex over (φ)}  (12b)

Projecting the acceleration along the negative {circumflex over (r)}-axis yields a positive centripetal acceleration:
S₁=−{circumflex over (r)}·{umlaut over ({right arrow over (r)}₁=r₁{dot over (φ)}²+l₀{dot over (θ)}²cos β+l₀{umlaut over (θ)} sin β+G* cos φ  (13a)
S₂=−{circumflex over (r)}·{umlaut over ({right arrow over (r)}₂=r₂{dot over (φ)}²+l₀{dot over (θ)}²cos β+l₀{umlaut over (θ)} sin β+G* cos φ  (13b)
that includes the gravitational force G* which is the projection of the gravitational acceleration into the plane of motion along the axis of theclub200.

The differential mode and common mode signals are given as
g(t)=(r₁−r₂){dot over (φ)}²; and  (14a)
f(t)=l₀({dot over (θ)}²cos β+{umlaut over (θ)} sin β)+G* cos φ  (14b)
where the generic terms {umlaut over (X)}₀and Ÿ₀are replaced with explicit expressions in terms of the motion of the double pendulum. The two signals can therefore be written as,

$\begin{array}{cc}{\mathrm{<figure-callout\; label="S"\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">S</figure-callout>}}_1=f\left(t\right)+\frac{r_1}{r_1-{\mathrm{<figure-callout\; label="r"\; filenames="US08109816-20120207-D00005.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}g\left(t\right)& \left(15a\right)\\ {\mathrm{<figure-callout\; label="S"\; filenames="US08109816-20120207-D00005.png"\; state="\{\{state\}\}">S</figure-callout>}}_2=f\left(t\right)+\frac{r_2}{r_1-{\mathrm{<figure-callout\; label="r"\; filenames="US08109816-20120207-D00005.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}g\left(t\right)& \left(15b\right)\end{array}$

Determination of a Calculation Time Window

Impact with Actual Golf Ball

In a preferred embodiment, the calculation time window is determined by examining the contents ofring buffer342 which holds approximately 5 seconds of data. Signal processing anddisplay system390 receives data frominterface310 and continuously loads thecircular buffer342 with the data fromclub200. The signal processing anddisplay system390 continuously calculate the difference signal, g(t). When g(t) becomes larger than a preset threshold, typically 300-500 m/s², the system acknowledges that a swing is occurring by generating a trigger. This magnitude of signal only happens during the downswing in the vicinity of the ball.Buffer342 continues to store data for about 2.5 seconds so that the trigger point can be substantially centered inbuffer342 with approximately 2.5 seconds of data on either side of the trigger point. The contents of the buffer then includes a complete data set for analysis of the golf swing.

The actual time of impact is preferably determined by calculating the derivative of the difference signal, g(t), and comparing this value to a reference level (impact threshold) of order of −5 g/sampling period (i.e. −5 g/4.42 msec), which is large in magnitude and negative in sign. When the derivative of g(t) is more negative than this reference level at a point in time after the trigger threshold, an impact has occurred.

When a real ball is hit the transfer of momentum fromclub head230 to the ball causes a sharp discontinuity in g(t) and therefore a spike in the derivative in g(t). The point of impact (378 inFIG. 11) defines the end of the integration interval for the calculations described herein. The start of the swing is determined as described in the following paragraph.

The beginning of the backswing swing and the transition from backswing to downswing is preferably determined by having the signal processing anddisplay system390 search throughbuffer342, working backward in time from the point of impact looking for two points at which {dot over (φ)}_i, (from Eq. 16 below) equals 0; the first point (376 inFIG. 11) being where the backswing transitions to a downswing and the second point being the beginning of thebackswing374 inFIG. 11. The point at which the swing begins, i.e. the beginning of the backswing, is taken as the origin of time, t=0.

Impact with Simulated Ball

In an alternate embodiment a simulated ball, one of plastic for example, is used to further improve the practice process. As would be known to one skilled in the art, the plastic ball being of very low mass would not substantially affect readings fromaccelerometers220 and225 and or a change inclub head230's momentum at impact. The impact does however generate an acoustic spike and this spike is sense by a microphone near the ball and fed directly to signal processing anddisplay390 to initiate an interrupt. This interrupt inserts a marker into the data stream received frominterface310. An advantage of this latter approach is that if desired, positional data can be developed into the follow through of the swing. The start of the swing is determined as before by having signal processing anddisplay system390 search backwards through thebuffer342 from the point of “impact” looking for a second data point at which {dot over (φ)}_i, (from Eq. 16 below) yields 0; the first point being where a backswing transitions to a downswing.

Determination of Club Positional Information

An object of the present invention is to use the values of S₁and S₂to determine θ(t) and φ(t) and therefore the position and timing associated with a swing ofgolf club200.

External means are preferably used to determine the initial values φ(0)=φ_i, θ(0)=θ_i, from which one calculates β_i=θ_i−φ_i. These can be determined through direct measurement, video analysis, or various other techniques known to those skilled in the art. Generically, φ_iis constrained relatively close to zero, generally between 5 and 20 degrees. θ_iis likewise comparably constrained. It is assumed that the initial values of {dot over (φ)}_i={umlaut over (φ)}_i={dot over (θ)}_i={umlaut over (θ)}_iare all =0.

Since S₁−S₂=g(t), using equation (14a) we find that:

$\begin{array}{cc}\stackrel{.}{\varphi }=\pm \sqrt{\frac{S_1-S_2}{r_1-{\mathrm{<figure-callout\; label="r"\; filenames="US08109816-20120207-D00005.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}}.& \left(16\right)\end{array}$
where the separation between accelerometers, r₁−r₂is know at time of manufacture; and the sign convention is negative in the backswing and positive in the downswing. Using the initial conditions described above, {dot over (φ)}(t) is integrated to yield φ(t)

It has been determined that providing an accurate determination of f(t) from the expressions for S₁and S₂given in equations 13a and 13b is non-trivial in a practice or playing environment because it is not readily apparent around which point, R₀the club rotates. Since r₁and r₂are measured relative to this point of rotation, the point must be known with reasonable accuracy if the resulting calculation of f(t) is to be useful in a calculation of θ(t) and φ(t).

It is reasonable to assume that this point R₀is between the hands, but exactly where the golfer grips the club can vary from shot to shot and locating this point somewhere within the hands can introduce errors on the order 10-15% due to the spatial extent of the grip. This problem is solved by the present invention by using the hardware described above and software based on the development below.

As shown above, S(t) is of the form S(t)=f(t)+αg(t) and g(t) is obtained by taking the difference S₁−S₂. However we do not know either α or f(t). The preferred embodiment for determining α is to minimize the quantity ∫[S(t)−αg(t)]²dt. Taking a derivative with respect to α and rearranging yields the expression:

$\begin{array}{cc}a=\frac{\int S\left(t\right)g\left(t\right)dt}{\int {g\left(t\right)}^{2}dt}.& \left(17\right)\end{array}$
where the integrations are performed over the time interval discussed above.
Using this expression for α, f(t)=S(t)−αg(t) (Eq. 17a) is determined. This is done for S₁and S₂. The resulting values of α are then used to calculate r₁and r₂.

FIGS. 7(a) and7(b) display the result of this calculation using the same data set used to generateFIG. 4. The data inFIG. 7(a) is the result for g(t) and the data inFIG. 7(b) is the result for f(t). From g(t) many details about the timing of the swing can be determined, such as the duration of the backswing and downswing. Furthermore, g(t) is intuitively interpreted as the motion of the golf club. While f(t) does not have a simple and intuitive interpretation, the inventor has found that there is substantial information contained in this signal. For example f(t) primarily yields information about the motion of the point about which the club is rotating. In the present invention this is the motion of the hands. Importantly f(t) also shows at380 and382 of FIG.11_the maximum and minimum value of the common mode signal during “release” as well position of “release” events relative to ball impact. The aforementioned golf swing parameters, among others, are important indicators of golf swing quality.

With f(t) determined, the invention uses Eq. 14b to solve for θ(t). The value of G* is preferably determined from the value of f(t) just prior to the beginning of the swing, when {dot over (θ)}(t) and {umlaut over (θ)}(t) are assumed to be zero and φ_iis known. Having previously determined φ(t) from g(t), one can now reliably subtract G* cos φ from f(t), yielding
ξ(t)=l₀({dot over (θ)}²cos β+{umlaut over (θ)} sin β)  (18)
Eq. 18 is used as an update equation to solve for θ(t). Given θ(t). {dot over (θ)}(t) and {umlaut over (θ)}(t) one determines {umlaut over (θ)}(t+dt), {dot over (θ)}(t+dt) and θ(t+dt) as follows:
Define the parameter ε such that,

$\begin{array}{cc}\ddot{\theta }\left(t+\mathrm{dt}\right)=\ddot{\theta }\left(t\right)+\varepsilon ;& \left(18a\right)\\ \stackrel{.}{\theta }\left(t+\mathrm{dt}\right)=\stackrel{.}{\theta }\left(t\right)+\left(\frac{\ddot{\theta }\left(t+\mathrm{dt}\right)+\ddot{\theta }\left(t\right)}{2}\right)\mathrm{dt};\mathrm{and}& \left(18b\right)\\ \theta \left(t+\mathrm{dt}\right)=\theta \left(t\right)+\left(\frac{\stackrel{.}{\theta }\left(t+\mathrm{dt}\right)+\stackrel{.}{\theta }\left(t\right)}{2}\right)\mathrm{dt}& \left(18c\right)\end{array}$
To simplify the equations we define the parameters:

$\begin{array}{cc}{\stackrel{.}{\theta }}_0=\stackrel{.}{\theta }\left(t\right)+\ddot{\theta }\left(t\right)\mathrm{dt}& \left(19a\right)\\ {\mathrm{<figure-callout\; label="\theta "\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">\theta </figure-callout>}}_0=\theta \left(t\right)+\stackrel{.}{\theta }\left(t\right)\mathrm{dt}+\ddot{\theta }\left(t\right)\frac{{\mathrm{<figure-callout\; label="dt"\; filenames="US08109816-20120207-D00005.png"\; state="\{\{state\}\}">dt</figure-callout>}}^2}{2}& \left(19b\right)\end{array}$
Rewriting Eqs. 18(a), 18(b), and 18(c) above, gives

$\begin{array}{cc}\stackrel{.}{\theta }\left(t+\mathrm{dt}\right)={\stackrel{.}{\theta }}_0+\mathrm{dt}\frac{\varepsilon }{2}& \left(20a\right)\\ \theta \left(t+\mathrm{dt}\right)={\mathrm{<figure-callout\; label="\theta "\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">\theta </figure-callout>}}_0+{\mathrm{<figure-callout\; label="dt"\; filenames="US08109816-20120207-D00005.png"\; state="\{\{state\}\}">dt</figure-callout>}}^2\frac{\varepsilon }{4}& \left(20b\right)\end{array}$
Inserting these expressions into Eq. 18 above, one obtains

$\begin{array}{cc}\frac{\xi \left(t+\mathrm{dt}\right)}{{\mathrm{<figure-callout\; label="l"\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">l</figure-callout>}}_0}=\left({\ddot{\theta }}_0+\varepsilon \right)\sin \left({\mathrm{<figure-callout\; label="\beta "\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">\beta </figure-callout>}}_0+\varepsilon \frac{{\mathrm{<figure-callout\; label="dt"\; filenames="US08109816-20120207-D00005.png"\; state="\{\{state\}\}">dt</figure-callout>}}^2}{4}\right)+{\left({\stackrel{.}{\theta }}_0+\varepsilon \frac{\mathrm{dt}}{2}\right)}^2\cos \left({\mathrm{<figure-callout\; label="\beta "\; filenames="US08109816-20120207-D00004.png,US08109816-20120207-D00005.png"\; state="\{\{state\}\}">\beta </figure-callout>}}_0+\varepsilon \frac{{\mathrm{<figure-callout\; label="dt"\; filenames="US08109816-20120207-D00005.png"\; state="\{\{state\}\}">dt</figure-callout>}}^2}{4}\right)& \left(21\right)\end{array}$
where we have defined β₀=θ₀−φ(t+dt). Expanding the above equation to first order in ε yields the preferred expression

$\begin{array}{cc}\varepsilon =\frac{\frac{\xi \left(t+\mathrm{dt}\right)}{l_0}-{\ddot{\theta }}_0\sin {\beta }_0-{\stackrel{.}{\theta }}_0^2\cos {\beta }_0}{\sin {\beta }_0+\mathrm{dt}{\stackrel{.}{\theta }}_0\cos {\beta }_0+\frac{{\mathrm{<figure-callout\; label="dt"\; filenames="US08109816-20120207-D00005.png"\; state="\{\{state\}\}">dt</figure-callout>}}^2}{4}\left({\ddot{\theta }}_0\cos {\beta }_0-{\stackrel{.}{\theta }}_0^2\sin {\beta }_0\right)}& \left(22\right)\end{array}$
This value of ε is then used in equations 18(a), 18(b) and 18(c) to determine θ(t+dt).{dot over (θ)}(t+dt), and {umlaut over (θ)}(t+dt).

In alternate embodiments, Eq. 22 can be solved to higher order in ε if increased numerical precision is deemed necessary.

The above methodology is used to determine θ(t) and φ(t) over some range of time. The starting point is the beginning of the swing. The starting parameters, φ_iand θ_i, are inputs to the calculation. In the preferred embodiment the final points, φ_fand θ_f, are where the club impacts the ball, though in alternate embodiments one could perform the calculation over any region of time during which one has valid data for S₁and S₂.

The values of the final points φ_fand θ_fare sensitive to the various independent parameters used in the calculation, φ_i, θ_i, r₁, r₂, and l₀. As is described above, φ_iand θ_ican be measured precisely at the start of the swing. The values r₁and r₂are determined as a byproduct of the calculation for f(t). The only remaining independent parameter in this analysis is l₀.

The preferred embodiment uses l₀as an adjustable parameter to enforce physically plausible endpoints for φ_fand θ_f. In the preferred embodiment the condition β_f≈β_iis enforced, though one could use any condition, including those determined through video analysis. In practice, the calculation starts by using an estimated value of l₀to calculate θ(t) and φ(t). The final points φ_fand θ_fare determined and β_fis compared to β_i. Based on this result, l₀is adjusted so as to decrease the difference |β_f−β_i| and the calculation is performed again. This loop is continued until one obtains the result and performs a loop test that varies l₀until equation 22 gives and update value that leads to a result that gives β_fsubstantially equal to β_i. In a preferred embodiment the allowable range of l₀relative to the estimated value of l₀is +/−10-20%. If for some reason l₀does not converge to a value that is within the range of +/−10-20%, the swing is repeated.

Display of φ(t) and θ(t)

Shown inFIG. 9 are the calculated values of φ(t) and θ(t) as a function of time for the conditions β_i=β_f=10.5 degrees. The final value for l₀is 0.48 meters, which is consistent with the estimate of 0.5±0.05 meters used for the analysis forFIG. 9. The maximum speed at impact was calculated to be 84 miles per hour, which is consistent with our separate measurement of 82 miles per hour measure which was checked with a commercial radar speed detector.

The orientation of the upper and lower portions of the double pendulum in an x-y coordinate system as a function of time is shown inFIG. 10. The axes are calibrated in units of meters.

FIG. 11 shows a preferred graphical display area362 (shown inFIG. 3) for displaying golf swing and invention control parameters. Included inFIG. 11 are raw and reduced data collected and processed by the present invention. Operation of thegraphical display area362 of the present embodiment is preferably programmed in the C# programming language within the Microsoft Visual Studio programming environment.

Display area362 includes control parameters “Threshold”, “Swing Max” and “Release Max” (expressed in g's) which are shown at368 and used for scalinggraphic displays364,372, and370. Also generally shown at368 is a “System Messages” area which displays certain swing parameters. In the preferred embodiment cursor positions374,376 and378 identify start of backswing, start of downswing and impact respectively, whilepositions380 and382 are used to define the change in common mode acceleration at “release”. These cursor positions are determined automatically based on internally set thresholds and time based criteria. In an alternate embodiment cursor position are set manually for alternative analysis protocols.

Graph364 is labeled “Swing Kinetics”, and provides a real-time representation of the difference between the outputs ofaccelerometers220 and225 which is the differential signal, g(t).Graph370 is labeled “Swing” and also represents g(t) but is presented with an expanded time axis so that acceleration values near ball impact are more clearly visible. Graph371 is labeled “Release” and represents the common mode signal f(t). Cursor positions380 and382 mark the minimum and maximum values f(t) before the impact.Graph370 andgraph372 are displayed afterthreshold366 ingraph364 is exceeded and thegraph364 is completed; that is, a full data set is collected. In an alternate embodiment,display area362 includes the double pendulum representation of the golf swing modeled inFIGS. 10aand10b. The particular set of graphs to be displayed are chosen from a drop down menu not shown inFIG. 11.

In a preferred embodiment the present invention calculates and displays in themessage area368 ofFIG. 11 the length of the backswing and the length of the downswing based on time values atcursor positions376—time atcursor position374. Also displayed is the g value of release which is the peak to peak intensity of f(t) in the vicinity of the swing just before impact and is the difference of the common mode signal (f(t)) betweencursor positions380 and382. Likewise maximum differential mode acceleration (g(t)) as well as ball impact are shown atcursor position378.

The methods of the present invention are not limited to the sport of golf. In fact the methods apply to any analysis of motion of a substantially rigid shaft about a pivot point where accelerometers mounted at positions along the shaft are used to calculate shaft dynamics and the positions of the accelerometers relative to the pivot point are not accurately known.

One skilled in the art would therefore recognize that the methods of the present invention are applicable to an analysis of the dynamics associated with baseball/softball (throwing and batting), tennis, bowling and fishing, among others, which are all readily able to be studied using the methods of the present invention.

Moreover, one skilled in the art would recognize that given the details of motion identified by the methods of the present invention and the physical characteristics of a golf club, bat, or any elongated member, one can also readily find the torque exerted on the club, bat or elongated member.

While the invention has been particularly shown and described with respect to preferred embodiments thereof, it will be understood by those skilled in the art that changes in form and details may be made therein without departing from the scope and spirit of the invention. For example, unless specifically recited in the claims, the order in which the claimed steps are performed is not material to the present invention, and therefore, again, unless explicitly recited, the order set forth in the claims is for convenience purposes only and not in any limiting sense.

Claims (18)

1. A method for analyzing at least one golf swing parameter using a plurality of accelerometers located proximate distal ends of a golf club, a signal processing and display system utilizing a double pendulum model of a golf club swing, said model for describing swing parameters and having an upper portion, a pivot point and a lower portion, the method comprising the steps of:

entering initial swing conditions and golf club parameters;

performing a swing and collecting data from the accelerometers;

determining a differential mode signal from the acceleration data;

calculating the pivot point location relative to each accelerometer using the accelerometer data;

calculating a common mode signal using the pivot point; and

determining at least one golf swing parameter as a function of time using the common mode signal;

wherein at least one of the determining steps or at least one of calculating steps are preformed by at least one of a microprocessor and personal computer.

2. The method as claimed inclaim 1, wherein the step of calculating the pivot point location relative to each accelerometer comprises the step of minimizing the contribution of the common mode signal into an accelerometer signal comprising the differential mode signal and the common mode signal.

3. The method as claimed inclaim 1, including the step of displaying the at least one golf swing parameter.

4. The method as claimed inclaim 3, wherein the step of displaying the at least one golf swing parameter includes displaying the common mode and differential mode signals.

5. The method as claimed inclaim 3, wherein the step of displaying golf swing parameters includes displaying positions of the upper and lower portions of the double pendulum model.

6. A method for analyzing at least one golf swing parameter using (i) an instrumented golf club having two accelerometers located at proximate respective distal ends of a golf club, (ii) data collection means and (iii) computer analysis means running a program based on a double pendulum model of a golf club swing, the method comprising the steps of:

entering initial swing conditions and golf club parameters;

performing a swing and collecting data from the accelerometers;

determining a differential mode signal from the acceleration data;

calculating a pivot point location relative to each accelerometer using the accelerometer data;

calculating a common mode signal using the pivot point; and

determining at least one golf swing parameter as a function of time using the common mode signal;

wherein at least one of the determining steps or at least one of calculating steps are preformed by at least one of a microprocessor and personal computer.

7. The method as claimed inclaim 6, wherein the step of calculating the pivot point location relative to each accelerometer comprises the step of minimizing the contribution of the common mode signal into an accelerometer signal comprising the differential mode signal and the common mode signal.

8. The method as claimed inclaim 6, including the step of displaying the at least one golf swing parameter.

9. The method as claimed inclaim 8, wherein the step of displaying the at least one golf swing parameter includes displaying the common mode and differential mode signals.

10. The method as claimed inclaim 8, wherein the step of displaying golf swing parameters includes displaying positions of the upper and lower portions of the double pendulum model.

11. A method for analyzing at least one motion parameter of an elongated member moving relative to a pivot point using a plurality of accelerometers located at proximate distal ends of the elongated member, a signal processing and display system utilizing a model relating the motion of the pivot point and accelerometers to a reference point, the method comprising the steps of:

entering initial positional and physical parameters of the elongated member;

moving the elongated member about the pivot point and collecting data from the accelerometers;

determining a differential mode signal from the acceleration data;

calculating the pivot point location relative to each accelerometer using the accelerometer data;

calculating a common mode signal using the pivot point location relative to each accelerometer; and

determining at least one parameter of motion for the elongated member as a function of time using the common mode signal;

wherein at least one of the determining steps or at least one of calculating steps are preformed by at least one of a microprocessor and personal computer.

12. The method as claimed inclaim 11, wherein the step of calculating the pivot point location relative to each accelerometer comprises the step of minimizing the contribution of the common mode signal into an accelerometer signal comprising the differential mode signal and the common mode signal.

13. The method as claimed inclaim 11, including the step of displaying the at least parameter of motion for the elongated member.

14. The method as claimed inclaim 13, wherein the step of displaying the at least one parameter of motion includes displaying the common mode and differential mode signals.

15. A method for analyzing at least one motion parameter of a swinging elongated member using a plurality of accelerometers located at proximate distal ends of the elongated member, a signal processing and display system utilizing a double pendulum model of the swinging elongated member, said model having an upper portion, a pivot point and a lower portion, the method comprising the steps of:

entering initial positional and physical conditions of the elongated member;

swinging the elongated member and collecting data from the accelerometers;

determining a differential mode signal from the acceleration data;

calculating the pivot point location relative to each accelerometer using the accelerometer data;

calculating a common mode signal using the pivot point location relative to each accelerometer; and

determining at least one motion parameter of the elongated member as a function of time using the common mode signal;

wherein at least one of the determining steps or at least one of calculating steps are preformed by at least one of a microprocessor and personal computer.

16. The method as claimed inclaim 15, wherein the step of calculating the pivot point location relative to each accelerometer comprises the step of minimizing the contribution of the common mode signal into an accelerometer signal comprising the differential mode signal and the common mode signal.

17. The method as claimed inclaim 15, including the step of displaying the at least parameter of motion for the elongated member.

18. The method as claimed inclaim 17, wherein the step of displaying the at least one parameter of motion includes displaying the common mode and differential mode signals.

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